Field
This disclosure relates to image processing, and more specifically, to data reconstruction and imputation of missing data.
Description of the Related Art
The technique of geometric harmonics was introduced as a method of extending empirical functions defined on a dataset in the form of a point cloud.
The term “geometric harmonics” refers to an eigenbasis for an incomplete Gram matrix, constructed empirically by means of a variant of what is known by those skilled in the art as the Nystrom method. The Nystrom method is a quadrature rule that allows a solution to an integral equation to be approximated by subsampling in which the integral is replaced by a sum of function values, where the function is evaluated on sample points weighted according to the quadrature rule.
When data is missing for any of a various reasons, it is difficult to reconstruct. Discarding incomplete data is a poor choice, as it can easily bias the remaining data or leave the analyst with too little data for a proper analysis or rendering. The present state-of-the-art technique for dealing with missing data is known as multiple imputation, in which multiple complete versions of the data are simulated by filling in missing entries in a purely stochastic manner. The analyses of different simulated versions are then averaged or pooled. This essentially linear technique does not perform well when the data has a strongly nonlinear structure. In addition, other techniques for imputation of missing data require some portion of the dataset to be intact. The intact subset of the data is called a “training set”. The method described herein is distinguishable in that it can be applied when no training set is available.
Throughout this description, elements appearing in figures are assigned three-digit reference designators, where the most significant digit is the figure number and the two least significant digits are specific to the element. An element that is not described in conjunction with a figure may be presumed to have the same characteristics and function as a previously-described element having a reference designator with the same least significant digits.